Geodesic
Proof of the Completeness of Darboux Wronskian Formulae for Order Two
Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 655-674

Voir la notice de l'article provenant de la source Cambridge University Press

Darboux Wronskian formulas allow us to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one, cannot be represented this way. It has been a long-standing problem to discover what other exceptions exist. In our previous work we proved that among transformations of total order one there are no other exceptions. Here we prove that for transformations of total order two there are no exceptions at all. We also obtain a simple explicit invariant description of all possible Darboux transformations of total order two.
DOI : 10.4153/CJM-2012-026-7
Mots-clés : 53Z05, 35Q99, completeness of Darboux Wronskian formulas, completeness of Darboux determinants, Darboux transformations, invariants for solution of PDEs 
Shemyakova, E. Proof of the Completeness of Darboux Wronskian Formulae for Order Two. Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 655-674. doi: 10.4153/CJM-2012-026-7
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